Given the functions \( f(x) = x - 5 \) and \( g(x) = x^2 - 1 \), you can perform various operations or analyses. Here are a few possibilities:

1. **Evaluate the functions at specific values of \( x \)**:
   - For example, find \( f(2) \) or \( g(3) \).
   
2. **Compose the functions**:
   - Find \( (f \circ g)(x) \), which means \( f(g(x)) \).
   - Find \( (g \circ f)(x) \), which means \( g(f(x)) \).

3. **Find the inverse of the functions**:
   - Determine \( f^{-1}(x) \) or \( g^{-1}(x) \), if they exist.

4. **Solve equations involving the functions**:
   - For example, solve \( f(x) = g(x) \) or \( f(x) = 0 \).

5. **Graph the functions**:
   - Sketch the graphs of \( f(x) \) and \( g(x) \) on the same coordinate plane.

Would you like to perform any specific operation or analysis with these functions? 

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Here are five related questions to expand on the information:

1. What is the value of \( f(3) \) and \( g(2) \)?
2. How would you find \( (f \circ g)(x) \) and what is the result?
3. Can you determine the inverse of \( f(x) = x - 5 \)?
4. What are the solutions to the equation \( f(x) = g(x) \)?
5. How would you graphically represent \( f(x) \) and \( g(x) \) on the same set of axes?

**Tip:** When composing functions, remember to substitute the entire expression of one function into the other.

Analyze the functions f(x) = x - 5 and g(x) = x² - 1, exploring concepts like function composition, inverses, and solving equations. This problem is ideal for high school students (Grades 9-12) looking to deepen their understanding of algebraic functions.

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